Finite Group Databasebeta

← #11909915

Subgroups — #11909915

Order 1152.

2084 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5727C211yesmaximal, characteristic, complemented
4#10595400C212yesmaximal, complemented
5#10595380C212yesmaximal, complemented
6#10595348C212yesmaximal, complemented
7#10595347C212yesmaximal, complemented
8#10594444C212yesmaximal
9#10594411C214yesmaximal, complemented
10#10594387C212yesmaximal, complemented
11#10594335C212yesmaximal, complemented
12#10594319C214yesmaximal, complemented
13#10594317C212yesmaximal, complemented
14#10593974C211yesmaximal, characteristic
15C4×D3×Dic6C211yesmaximal, characteristic, complemented
16#10593863C211yesmaximal, characteristic, complemented
17#10593861C211yesmaximal, characteristic, complemented
18#86753—31nomaximal
19#86266—31nomaximal
20C2×C3×D3×Q8C2212yes—
21C2×D3×Dic6C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2212yes—
24#64153C2212yes—
25#64099C2212yes—
26#64098C2214yes—
27#64096C2212yes—
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C3×#946C2212yes—
31C3×#946C2212yes—
32C3×Q8×Dic3C2212yes—
33C3×#897C2212yes—
34C3×#896C2214yes—
35C3×#893C2212yes—
36C3×#892C2212yes—
37C3×#890C2212yes—
38C3×#888C2212yes—
39C3×#887C2212yes—
40C3×C4×D12C2211yescharacteristic
41C3×C42×D3C2211yescharacteristic
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C4×#627C2212yes—
45#63908C2211yescharacteristic
46#63905C2212yes—
47C4×#625C2212yes—
48#63891C2214yes—
49D3×C4⋊Dic3C2211yescharacteristic
50#63887C2214yes—
51#63879C2214yes—
52#63878C2214yes—
53D3×Dic3⋊C4C2212yes—
54C4×D3×Dic3C2212yes—
55#63872C2212yes—
56#63869C2211yescharacteristic
57#63867C2214yes—
58#63866C2212yes—
59#63863C2212yes—
60#63862C2214yes—
61#63860C2211yescharacteristic
62#63859C2212yes—
63#63859C2214yes—
64#63858C2214yes—
65#63858C2214yes—
66#63857C2212yes—
67#63857C2211yescharacteristic
68#63855C2212yes—
69#63855C2214yes—
70#63851C2214yes—
71#63846C2214yes—
72#63846C2214yes—
73#63845C2214yes—
74#63844C2211yescharacteristic
75#63843C2212yes—
76#63843C2214yes—
77#63843C2212yes—
78Dic3×Dic6C2214yes—
79Dic3×Dic6C2212yes—
80Dic3×Dic6C2211yescharacteristic
81#63841C2214yes—
82#63841C2212yes—
83#63839C2214yes—
84#63837C2212yes—
85C3×D4×Q8—31no—
86C3×#533—31no—
87Q8×#67—32no—
88#5812—32no—
89#5732—31no—
90#5728—32no—
91#5728D311yescharacteristic, complemented
92#5727D311yescharacteristic, complemented
93#5721—31no—
94#5721—31no—
95#5721—32no—
96#5721—31no—
97#5721—61no—
98#5696—34no—
99#5642—32no—
100#5639—32no—
101#5639—34no—
102#5632—32no—
103#5625—32no—
104#5625—34no—
105#5624—32no—
106#5622—32no—
107#5583—32no—
108#5572—32no—
109C4×D3×Q8—31no—
110#5570—31no—
111#5569—32no—
112#5568—32no—
113#5557—32no—
114#5557—31no—
115#5542—32no—
116#5542—31no—
117#5531—34no—
118#5479—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121C2×#634C2311yescharacteristic
122C2×#634C2311yescharacteristic
123C3×D3×Q8—28no—
124C2×C3×D12C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2314yes—
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2312yes—
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2314yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2312yes—
134C2×#625C2312yes—
135C2×D3×Dic3C2312yes—
136C2×D3×Dic3C2312yes—
137D3×Dic6—24no—
138C32×C4⋊C4C2312yes—
139C32×C4⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4⋊(C3⋊Dic3)C2314yes—
144#3750C2312yes—
145#3750C2312yes—
146#3750C2314yes—
147#3750C2314yes—
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2312yes—
150C4×C3⋊Dic3C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2312yes—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2314yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2312yes—
162C3×C4×Dic3C2311yescharacteristic
163C3×C4×Dic3C2314yes—
164C3×C4×Dic3C2312yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2311yescharacteristic
167#3724C2312yes—
168#3724C2312yes—
169Dic3⋊Dic3C2312yes—
170Dic3⋊Dic3C2314yes—
171Dic3⋊Dic3C2312yes—
172Dic3⋊Dic3C2312yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177(C2×D3)⋊Dic3C2312yes—
178(C2×D3)⋊Dic3C2314yes—
179(C2×D3)⋊Dic3C2312yes—
180(C2×D3)⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2312yes—
183Dic32C2312yes—
184Dic32C2312yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C22×C3×Q8—32no—
189C2×D3×Q8—31no—
190C2×D3×Q8C2×D312yes—
191C22×Dic6—31no—
192C3×C4⋊Q8—21no—
193C3×C4⋊Q8—32no—
194C3×C4⋊Q8—31no—
195C3×C4⋊Q8C2×D311yescharacteristic
196C3×C4⋊Q8C2×D311yescharacteristic
197C3×#125—32no—
198C3×C22⋊Q8—32no—
199C3×C22⋊Q8—32no—
200C3×C22⋊Q8—34no—
201C3×C22⋊Q8—32no—
202C3×C4×Q8—32no—
203C3×C4×Q8—32no—
204C3×C4×Q8—31no—
205C3×C4×D4—32no—
206C3×C4×D4—31no—
207C3×#117—32no—
208C2×C3×C42—31no—
209#947—32no—
210#946—34no—
211#946C2×D312yes—
212#946C2×D312yes—
213Q8×Dic3—32no—
214Q8×Dic3—32no—
215Q8×Dic3—34no—
216Q8×Dic3—32no—
217Q8×Dic3—32no—
218Q8×Dic3—34no—
219Q8×Dic3—32no—
220Q8×Dic3—31no—
221Q8×Dic3—62no—
222Q8×Dic3C2×D312yes—
223#944—32no—
224#944—32no—
225#944—34no—
226#944—32no—
227#944—62no—
228#938—31no—
229#936—32no—
230#936—31no—
231#930—31no—
232#929—32no—
233C4×#67—32no—
234C4×#67—32no—
235C4×#67—34no—
236#926—32no—
237#926—34no—
238#926—34no—
239#926—32no—
240C2×C4⋊Dic3—31no—
241#924—31no—
242#924—32no—
243#924—34no—
244C2×Dic3⋊C4—32no—
245C2×C4×Dic3—32no—
246#898—34no—
247#898—34no—
248#898—34no—
249#897—32no—
250#897—31no—
251#897C2×D312yes—
252#896—34no—
253#896C2×D314yes—
254#893C2×D312yes—
255#892—32no—
256#892—34no—
257#892—34no—
258#892C2×D312yes—
259D3×C4⋊C4—32no—
260D3×C4⋊C4—31no—
261#890—32no—
262#890—32no—
263#890—34no—
264#890—32no—
265#890—32no—
266#890—34no—
267#890—34no—
268#890—31no—
269#890—62no—
270#890C2×D312yes—
271#889—34no—
272#889—34no—
273#889—34no—
274#889—34no—
275#889—34no—
276#889—34no—
277#889—64no—
278#888—34no—
279#888C2×D312yes—
280#887—32no—
281#887—34no—
282#887—32no—
283#887—32no—
284#887—32no—
285#887—32no—
286#887—31no—
287#887—62no—
288#887C2×D312yes—
289#886—34no—
290#883—32no—
291#883—34no—
292#67⋊C4—34no—
293#879—34no—
294#879—34no—
295#879—34no—
296#879—34no—
297#879—32no—
298#878—34no—
299#877—34no—
300#876—32no—
301#876—34no—
302#875—31no—
303C4×D12C2×D311yescharacteristic
304#872—32no—
305#872—34no—
306C42×D3—32no—
307C42×D3C2×D311yescharacteristic
308#870—31no—
309#870—34no—
310#869—32no—
311#869C2×D311yescharacteristic
312C4×Dic6—32no—
313C4×Dic6—31no—
314C4×Dic6—34no—
315C4×Dic6—31no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—61no—
324C4×Dic6—61no—
325C4×Dic6C2×D311yescharacteristic
326C22×C3×D3C2412yes—
327C22×C3×D3C2411yescharacteristic
328C32×Q8—24no—
329C2×C32×C4C2411yescharacteristic
330C2×C32×C4C2414yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337#634—22no—
338#634—22no—
339C2×C3×Dic3C2411yescharacteristic
340C2×C3×Dic3C2414yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2412yes—
346C3×D12—22no—
347C3×C4×D3—22no—
348C3×C4×D3—22no—
349C3×C4×D3—24no—
350C3×C4×D3—22no—
351C3×C4×D3—28no—
352C3×Dic6—24no—
353C3×Dic6—28no—
354C3×Dic6#4114yes—
355#627—24no—
356#625—24no—
357D3×Dic3—24no—
358D3×Dic3—24no—
359#557—92no—
360#557—91no—
361#557—91no—
362#556—92no—
363#556—91no—
364#552—94no—
365#552—92no—
366D4×Q8—31no—
367D4×Q8—92no—
368#541—92no—
369#541—94no—
370#533—31no—
371#533—92no—
372#529—91no—
373#529—92no—
374#519—92no—
375C2×C4×Q8—91no—
376C2×C3×Q8—22no—
377C2×C3×Q8—31no—
378C2×C3×Q8—34no—
379C2×C3×Q8—32no—
380C2×C3×Q8—68no—
381C2×C3×Q8C22×D312yes—
382C2×C3×Q8C22×D312yes—
383C2×C3×D4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—34no—
387C22×C3×C4—32no—
388C22×C3×C4—31no—
389C2×#67—32no—
390C2×#67—32no—
391C22×Dic3—32no—
392C22×Dic3—32no—
393D3×Q8—28no—
394D3×Q8—64no—
395C2×D12C22×D311yescharacteristic
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3C22×D311yescharacteristic
399C2×C4×D3C22×D311yescharacteristic
400C2×C4×D3C22×D311yescharacteristic
401C2×C4×D3C22×D312yes—
402C2×C4×D3C22×D314yes—
403C2×Dic6—31no—
404C2×Dic6—31no—
405C2×Dic6—31no—
406C2×Dic6—31no—
407C2×Dic6—32no—
408C2×Dic6—32no—
409C2×Dic6—61no—
410C2×Dic6—61no—
411C2×Dic6—64no—
412C2×Dic6C22×D312yes—
413C2×Dic6C22×D314yes—
414C2×Dic6C22×D311yescharacteristic
415C3×C4⋊C4—22no—
416C3×C4⋊C4—22no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—32no—
420C3×C4⋊C4—31no—
421C3×C4⋊C4—32no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—34no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4C22×D312yes—
426C3×C4⋊C4C22×D312yes—
427C3×C4⋊C4C22×D312yes—
428C3×C4⋊C4C22×D312yes—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—32no—
431C3×C22⋊C4—34no—
432C3×C42—21no—
433C3×C42—32no—
434C3×C42—31no—
435C3×C42—31no—
436C3×C42—31no—
437C3×C42—34no—
438C3×C42C22×D311yescharacteristic
439C3×C42C22×D311yescharacteristic
440#217—32no—
441#217—32no—
442#217—34no—
443#217—32no—
444#217—34no—
445#217—32no—
446(C2×D3)⋊C4—32no—
447(C2×D3)⋊C4—32no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—32no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—32no—
452(C2×D3)⋊C4C22×D312yes—
453(C2×D3)⋊C4C22×D314yes—
454(C2×D3)⋊C4C22×D314yes—
455C4⋊Dic3—31no—
456C4⋊Dic3—31no—
457C4⋊Dic3—31no—
458C4⋊Dic3—34no—
459C4⋊Dic3—31no—
460C4⋊Dic3—34no—
461C4⋊Dic3—32no—
462C4⋊Dic3—32no—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3—34no—
466C4⋊Dic3—34no—
467C4⋊Dic3—32no—
468C4⋊Dic3—32no—
469C4⋊Dic3—61no—
470C4⋊Dic3—61no—
471C4⋊Dic3—64no—
472C4⋊Dic3C22×D311yescharacteristic
473C4⋊Dic3C22×D312yes—
474C4⋊Dic3C22×D312yes—
475C4⋊Dic3C22×D311yescharacteristic
476C4⋊Dic3C22×D314yes—
477Dic3⋊C4—32no—
478Dic3⋊C4—32no—
479Dic3⋊C4—32no—
480Dic3⋊C4—32no—
481Dic3⋊C4—34no—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—32no—
486Dic3⋊C4—32no—
487Dic3⋊C4—32no—
488Dic3⋊C4—32no—
489Dic3⋊C4—32no—
490Dic3⋊C4—34no—
491Dic3⋊C4—32no—
492Dic3⋊C4—32no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—32no—
497Dic3⋊C4—62no—
498Dic3⋊C4—62no—
499Dic3⋊C4—64no—
500Dic3⋊C4—64no—
501Dic3⋊C4C22×D312yes—
502Dic3⋊C4C22×D314yes—
503Dic3⋊C4C22×D314yes—
504C4×Dic3—32no—
505C4×Dic3—32no—
506C4×Dic3—32no—
507C4×Dic3—32no—
508C4×Dic3—34no—
509C4×Dic3—34no—
510C4×Dic3—32no—
511C4×Dic3—32no—
512C4×Dic3—34no—
513C4×Dic3—34no—
514C4×Dic3—34no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—34no—
518C4×Dic3—62no—
519C4×Dic3—62no—
520C4×Dic3—64no—
521C4×Dic3C22×D311yescharacteristic
522C4×Dic3C22×D312yes—
523C4×Dic3C22×D311yescharacteristic
524C4×Dic3C22×D311yescharacteristic
525C4×Dic3C22×D314yes—
526C22×C32C2511yescharacteristic
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D32−1+412yes—
533C32×C4—24no—
534C32×C4—21no—
535C32×C4C2×#4112yes—
536C32×C42−1+412yes—
537C3⋊Dic3—22no—
538C3⋊Dic3—22no—
539C3⋊Dic3—22no—
540C3⋊Dic3—22no—
541C3×Dic3—21no—
542C3×Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—24no—
545C3×Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3C2×#4114yes—
548C22×Q8—32no—
549C22×Q8—91no—
550C4⋊Q8—32no—
551C4⋊Q8—31no—
552C4⋊Q8—92no—
553C4⋊Q8—94no—
554C4⋊Q8—92no—
555C4⋊Q8D3211yescharacteristic
556#126—92no—
557#126—94no—
558#126—94no—
559#126—94no—
560#126—94no—
561#125—32no—
562#125—91no—
563#125—94no—
564#125—94no—
565#125—94no—
566#125—94no—
567#125—92no—
568#125—92no—
569#125—94no—
570#124—91no—
571#124—92no—
572#123—94no—
573#123—92no—
574C22⋊Q8—32no—
575C22⋊Q8—32no—
576C22⋊Q8—32no—
577C22⋊Q8—34no—
578C22⋊Q8—94no—
579C22⋊Q8—91no—
580C22⋊Q8—94no—
581C22⋊Q8—92no—
582#121—91no—
583C4×Q8—32no—
584C4×Q8—32no—
585C4×Q8—31no—
586C4×Q8—92no—
587C4×Q8—91no—
588C4×Q8—92no—
589C4×Q8—91no—
590C4×Q8—94no—
591C4×Q8—92no—
592C4×Q8—94no—
593C4×Q8—92no—
594C4×Q8—92no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×Q8—91no—
598C4×Q8—91no—
599C4×D4—32no—
600C4×D4—31no—
601C4×D4—94no—
602C4×D4—92no—
603#117—32no—
604#117—92no—
605#117—94no—
606#117—94no—
607#117—94no—
608#117—92no—
609C2×C4⋊C4—92no—
610C2×C4⋊C4—91no—
611C2×C42—31no—
612C2×C42—92no—
613C23×C3—31no—
614C23×C3—32no—
615C22×D3C23×D312yes—
616C22×D3C23×D311yescharacteristic
617C3×Q8—24no—
618C3×Q8—24no—
619C3×Q8—34no—
620C3×Q8—44no—
621C3×Q8—68no—
622C3×Q8—64no—
623C3×D4—62no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—24no—
627C2×C3×C4—21no—
628C2×C3×C4—32no—
629C2×C3×C4—31no—
630C2×C3×C4—32no—
631C2×C3×C4—34no—
632C2×C3×C4—32no—
633C2×C3×C4—31no—
634C2×C3×C4—31no—
635C2×C3×C4—68no—
636C2×C3×C4—62no—
637C2×C3×C4—62no—
638C2×C3×C4—62no—
639C2×C3×C4—64no—
640C2×C3×C4C23×D314yes—
641C2×C3×C4C23×D314yes—
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647C2×C3×C4C23×D311yescharacteristic
648#67—64no—
649#67—64no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—64no—
663C2×Dic3—64no—
664C2×Dic3C23×D311yescharacteristic
665C2×Dic3C23×D314yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D311yescharacteristic
669C2×Dic3C23×D311yescharacteristic
670C2×Dic3C23×D312yes—
671D12—22no—
672C4×D3—22no—
673C4×D3—24no—
674C4×D3—22no—
675C4×D3—22no—
676C4×D3—28no—
677C4×D3—64no—
678C4×D3—64no—
679Dic6—24no—
680Dic6—28no—
681Dic6—64no—
682Dic6—64no—
683Dic6—62no—
684Dic6—62no—
685Dic6—62no—
686Dic6—62no—
687Dic6—64no—
688Dic6—122no—
689Dic6#23714yes—
690C2×C32C22×#4111yescharacteristic
691C2×C32C2×2−1+411yescharacteristic
692C2×C32C2×2−1+411yescharacteristic
693C3×D3—22no—
694C3×D3—42no—
695C2×Q8—31no—
696C2×Q8—32no—
697C2×Q8—34no—
698C2×Q8—68no—
699C2×Q8—92no—
700C2×Q8—91no—
701C2×Q8—91no—
702C2×Q8—184no—
703C2×Q8C2×D3212yes—
704C2×D4—31no—
705C2×D4—92no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—34no—
710C22×C4—32no—
711C22×C4—92no—
712C22×C4—92no—
713C4⋊C4—32no—
714C4⋊C4—31no—
715C4⋊C4—32no—
716C4⋊C4—32no—
717C4⋊C4—34no—
718C4⋊C4—34no—
719C4⋊C4—31no—
720C4⋊C4—34no—
721C4⋊C4—92no—
722C4⋊C4—92no—
723C4⋊C4—92no—
724C4⋊C4—94no—
725C4⋊C4—92no—
726C4⋊C4—92no—
727C4⋊C4—94no—
728C4⋊C4—92no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—91no—
732C4⋊C4—92no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—91no—
736C4⋊C4—94no—
737C4⋊C4—92no—
738C4⋊C4C2×D3212yes—
739C4⋊C4C2×D3212yes—
740C22⋊C4—34no—
741C22⋊C4—34no—
742C22⋊C4—32no—
743C22⋊C4—92no—
744C22⋊C4—92no—
745C22⋊C4—94no—
746C22⋊C4—92no—
747C22⋊C4—92no—
748C22⋊C4—94no—
749C42—31no—
750C42—31no—
751C42—31no—
752C42—32no—
753C42—34no—
754C42—92no—
755C42—92no—
756C42—94no—
757C42—94no—
758C42—92no—
759C42—94no—
760C42—92no—
761C42C2×D3211yescharacteristic
762C22×C3—21no—
763C22×C3—32no—
764C22×C3—61no—
765C22×C3—61no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3C24×D311yescharacteristic
770C22×C3C24×D311yescharacteristic
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3#100712yes—
777C3×C4—24no—
778C3×C4—21no—
779C3×C4—24no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—34no—
784C3×C4—44no—
785C3×C4—41no—
786C3×C4—61no—
787C3×C4—62no—
788C3×C4—61no—
789C3×C4—64no—
790C3×C4—62no—
791C3×C4—61no—
792C3×C4C2×#23712yes—
793C3×C4#100712yes—
794C3×C4D3×#4112yes—
795C3×C4#101012yes—
796Dic3—22no—
797Dic3—21no—
798Dic3—21no—
799Dic3—24no—
800Dic3—21no—
801Dic3—22no—
802Dic3—64no—
803Dic3—62no—
804Dic3—62no—
805Dic3—62no—
806Dic3—62no—
807Dic3—62no—
808Dic3—62no—
809Dic3—62no—
810Dic3—62no—
811Dic3—122no—
812Dic3—122no—
813Dic3—122no—
814Dic3C2×#23714yes—
815C32#352311yescharacteristic, complemented, Sylow
816C23—31no—
817C23—32no—
818Q8—24no—
819Q8—34no—
820Q8—68no—
821Q8—64no—
822Q8—184no—
823Q8—182no—
824Q8—182no—
825D4—62no—
826D4—184no—
827C2×C4—32no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—34no—
832C2×C4—32no—
833C2×C4—32no—
834C2×C4—68no—
835C2×C4—62no—
836C2×C4—64no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—92no—
840C2×C4—92no—
841C2×C4—92no—
842C2×C4—92no—
843C2×C4—184no—
844C2×C4—184no—
845C2×C4C22×D3214yes—
846C2×C4C22×D3211yescharacteristic
847C2×C4C22×D3211yescharacteristic
848C2×C4C22×D3211yescharacteristic
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—62no—
853C2×C3—122no—
854C2×C3C22×#23711yescharacteristic
855C2×C3C2×#100711yescharacteristic
856C2×C3C2×#100711yescharacteristic
857C2×C3C2×D3×#4111yescharacteristic
858C2×C3C2×#101011yescharacteristic
859C2×C3D3×2−1+411yescharacteristic
860D3—22no—
861D3—42no—
862C22—32no—
863C22—61no—
864C22—61no—
865C22—62no—
866C22—62no—
867C22—62no—
868C22C23×D3211yescharacteristic
869C4—24no—
870C4—21no—
871C4—34no—
872C4—62no—
873C4—61no—
874C4—61no—
875C4—64no—
876C4—61no—
877C4—62no—
878C4—182no—
879C4—182no—
880C4—182no—
881C4—182no—
882C4D3×#23712yes—
883C4#6431512yes—
884C3—21no—
885C3#8626611yescharacteristic, complemented
886C3#8675311yescharacteristic, complemented
887C2—62no—
888C2—122no—
889C2C2×D3×#23711yescharacteristic
890C2C2×#6431511yescharacteristic
891C2D3×#100711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radical#63908C22
hypercenterC4⋊Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10596192C2semidirect
2. C3×#5728C2semidirect
3. C3×#5727C2semidirect
4. #10595400C2semidirect
5. #10595380C2semidirect
6. #10595348C2semidirect
7. #10595347C2semidirect
9. #10594411C2semidirect
10. #10594387C2semidirect
11. #10594335C2semidirect
12. #10594319C2semidirect
13. #10594317C2semidirect
15. C4×D3×Dic6C2semidirect
16. #10593863C2semidirect
17. #10593861C2semidirect
91. #5728D3semidirect
92. #5727D3semidirect
815. C32#3523semidirect
885. C3#86266semidirect
886. C3#86753semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105961922
C3×#57282
C3×#57272
#105954002
#105953802
#105953482
#105953472
#105944442
#105944112
#105943872
#105943352
#105943192
#105943172
#105939742
C4×D3×Dic62
#105938632
#105938612
#867533
#862663